From a uniform disc of radius `R`, a circular section of radius `R//2` is cut out. The centre of the hole is at `R//2` from the centre of the original disc. Locate the centre of mass of the resulting flat body.

Explanation

Let O is the centre of mass oforiginal disc.
`O_(1)` is CM of the portion cut out.
`O_(2)` is the CM of remaining protion.
Let m is mass per unit area of disc
Mass of original disc `M=piR^(2)m`
Mass of circular hole out `=M.=pi((R)/(2))^(2))m`
`=(pi)/(4)R^(2)m`

Mass of remaining part `M..=piR^(2)m-(pi)/(4)R^(2)m`
`=(3)/(4)piR^(2)m`
M and M" are supposed to be concentrated at O and O, respectively.
If O is the centre of mass of M. and M" then Moment of Mabout Moment of M" about O.
`M.=O_(1)O=M..O_(2)O`
`(pi)/(4)R^(2)m(R)/(2=(3)/(4)piR^(2)mO_(2)O`
`O_(2)O=(R)/(6)`